However I don't understand how exactly hypothesis tests help to solve the philosophical problems with induction.

I don't think it does, in fact I'm not claiming that in my post. I'm trying to set up hypothesis testing as a way of doing induction without trying to solve the problem of induction.

I don't think hypothesis testing would resolve disagreements among competing paradigms either - well maybe it could, but I'm not talking about that.

(I think you're largely correct about why, in actual fact, hypothesis testing is used. There's also some element of inertia as well)

My understanding of standardised hypothesis tests was that they serve the purposes of

1. avoiding calculations dependent on details of the alternative hypothesis
2. providing objective criteria to decide under uncertainty

There are practical reasons for both purposes. (1) is useful because the alternative hypothesis is usually more complex than the null and can have lots of parameters, thus calculating probabilities under the alternative may become impossible, especially with limited computing power. As for (2), science is a social institution - journal editors need a tool to reject publishing unfounded hypotheses without risk of being accused of having "unfair" priors, or whatever.

However I don't understand how exactly hypothesis tests help to solve the philosophical problems with induction. Perhaps it would be helpful to list several different popular philosophical approaches to induction (not sure what are the major competing paradigms here - perhaps Bayesianism, falsificationism, "induction is impossible"?), present example of problems where the proponents of particular paradigms disagree about the conclusion, and show how a hypothesis test could resolve the disagreement?

It seems almost self-evident that (barring foreign subjugation) a government will care about the wants of (some of) its citizens and nothing else: no other object of concern is plausible.

This is not at all "self-evident", unless you choose to interpret the sentence completely literally, which would render it nearly meaningless.

For example, the government of North Korea does indeed care about the wants of "some" of its citizens, where the number of such citizens is pretty close to 1.

Isn't that steel-man, rather than strong-man?

divine quote of gay Turing

I'm not sure I know how to parse this.

Even God can quote Bayes when it suits him.

Still upvoted for raw cleverness, though.

I wonder how this works with dating?

I think I once saw a comment by someone stating that they had a policy of systematically downvoting all comments containing an emoticon, except exceptionally good ones.

So, apparently LessWrong feels unfriendly. This is something I've heard several times, so I'll accept it as correct. (I don't get that feeling myself, but I wouldn't expect to notice it anyway.) What are some Internet forums that don't feel unfriendly, and what do they do there that we don't do on LessWrong? Talk about ourselves and our lives - "small talk", in other words?

Yes, I think that you and I are talking about the same thing.

Attempting to rephrase, In essence, my question is how specific do I have to make my number, function, terminating algorithm, or noncomputable algorithm.

Clearly 99999999 is valid as a number,

And presumably 3^^^^3 as a function,

But is a program "Hyper G" that generates a number using a terminating algorithm involving Graham's number being Knuth up arrowed to Graham's number, having the result stored in a variable, and then having the variable Knuth up arrowed to itself iteratively until the process has repeated Graham's number times valid as a terminating algorithm?

Is "The result of the Busy Beaver Function of a Turing Machine with Hyper G States and Hyper G symbols" valid? You might be able to say that names a large integer, but since it isn't even a computable function anymore. I don't know if Omega would accept that as an answer.